Engine starts when primed but stops in seconds. When you push the primer button five times and then pull the rope, the engine starts, but then kills. It's a 6.5 hp on a Toro Recycling GTS mower. I ran it dry last fall, then stored it in a pole barn.

Press primer bulb 6 times
Move throttle lever to start position
Move choke lever to full choke position
Pull starter rope sharply until engine attempts to start, but no more than 5 pulls.
Move choke lever to half choke position. Pull starter rope sharply engine runs. If engine hasn't started after 5 pulls, repeat all steps above.
After warming up for 10 seconds, move choke lever to run position.

Manuallib.com has a manual for this model available for free download

Try pulling the rope slowly until the starter engages the flywheel (you should feel when it engages) then give a good pull to start the engine. Don't give the rope a quick hard pull in one motion. You will probably need to do this three or four times before the engine starts. Of course push the primer button the number of times called for in your engine instructions before trying to start the engine. If you still don't think the starter is engaging the flywheel if would take it back where you bought it if it's new.

There is no trick, push the primer button as many times as it takes to 3/4 fill the bulb ( you cannot over prime it no matter how many times you push it ) pull the red start switch out and at the same time lift up until it locks up, crank the engine twice or until it fires, do not continue to crank, push the red stop button down half way, crank engine until it starts and runs, blip the trigger to bring to idle.

The procedure for starting an engine is as follows:

• Check that you have the throttle in the start position and/or on high revs with choke on
  
• Prime the engine by pushing the button about 5 times
• Pull out the cord until you meet resistance. Then let the cord go fully back into the engine and then pull the cord out sharply. Repeat this until the engine starts but not more than a few times.
• If the engine doesn't start, try pressing the primer button another few times then try to pull start the engine
• If the engine doesn't start after a few pulls it may have flooded so leave it for a few minutes before pulling the starter rope
  

O and I are the international symbols for off and on. The O is the off position and the I is the on position. Put the switch in the I position. Make sure there is properly mixed fuel in the tank. Your Mantis probably uses fuel mixed 1 part 2cycle oil to 50 parts gasoline. Push the primer bulb a few times until you see fuel in the bulb. Position the choke lever to full choke, open the throttle completely and use short, quick pulls on the rope until the engine sputters. Reposition to choke to half and pull the rope again. The engine should start at this time. Let the engine run for a few seconds, then push the choke lever to off. Go to work in the garden.
Good luck!

What's happening is your carburetor's losing its prime. You may have a leak in the diaphragm, but if you're starting your mower for the first time of the year, it may just have all leaked down and is having troubles pulling the fuel up. Here's what to do. Take the air cleaner off, set it someplace away from the mower, and press the primer bulb about 4 times. Pull the rope, and as soon as it starts to get running, put your hand over the top of the carburetor so that you create a seal on it. You will kill your mower by doing this, but the vacuum from the engine trying to pull air in while your hand is there will fill the carb with fuel and get air, bad fuel, condensation, etc out. You should then be able to start your mower and keep it running. If this doesn't work, you'll probably have to put a new diaphragm in the carburetor, as yours likely has lost its seal, but that's if my method doesn't work.

The jet in the carburetor is clogged if it is a 4 cycle unit or the diaphragms are stiff if in a 2 cycle unit. It is burning the primed fuel but can not draw any more fuel to burn to stay running.
HTH
Good Day

take bowl off bottom of carb....clean and reassemble

Drain float bowel
check for water .

i dont understand the pulling the button - do you mean push the primer button - if you mean primer button it sounds like the high speed jet in the carb is dirty and needs service- you can attempt to start and once engine fires have someone continually push primer to keep running it ma clear the blockage - did You check the fuel tank for any water ?